Conversion of over-the-counter swaps to standardized forward swaps

ABSTRACT

Systems, processes and methods are described for converting over-the-counter derivative products such as interest rate swaps (IRSs) to standardized forward swaps, such as centrally cleared interest rate swaps. The value of each leg of the over-the counter swap may be determined and compared to a value of a corresponding leg of the forward swap. A mark-to-market value may be determined as the difference between the values.

CROSS-REFERENCE TO RELATED APPLICATIONS

This patent is related to co-pending U.S. patent application Ser. No.11/950,117, filed on Dec. 4, 2007, titled “FACTORIZATION OF INTERESTRATE SWAP VARIATION”, the content of which is incorporated in itsentirety herein by reference for all purposes.

TECHNICAL FIELD

This patent generally relates to systems and processes for theadministration of financial instruments, and more specifically toconversion of over-the-counter swap positions to centrally cleared swappositions.

BACKGROUND

Over-the-counter (OTC) financial products include financial instrumentsand investment vehicles that are bought, sold, traded, exchanged, and/orswapped between counterparties. After an exchange of an OTC financialproduct, the parties may expend resources managing the product for theduration of its life. Management may be complicated based on the numberof exchanges and/or the specific terms of the contract.

Interest rate swaps (IRS) are examples of financial products that aretraditionally exchanged, traded or otherwise bought and sold in an OTCmarket. The IRS is a financial product or investment vehicle where theparties agree to exchange streams of future interest payments based on aspecified principal or notional amount. Each stream is typicallyreferred to as a leg.

An example of an IRS is a plain fixed-to-floating, or “vanilla,”interest rate swap. The vanilla swap includes an exchange of two streamsof payments, where one stream is based on a floating or variableinterest rate and the other is based on a fixed interest rate. Thevariable interest rate may be linked to a periodically known or agreedupon rate for the term of the swap, such as the London Interbank OfferedRate (LIBOR). The variable rate may be based on other agreed uponfactors such as a reference rate, the total return of a swap, aneconomic statistic, etc. Other examples of swaps include total returnswaps, and Equity Swaps.

The expiration or maturity of the streams of payments may occur wellinto the future. A book of existing and new IRS may include multiple IRShaving a variety of maturity dates. In the OTC market, the parties to anIRS, such as banks and intermediaries, each bear the risk and expense ofcarrying the IRS over the lifetime of the swap. Typically, a party mayreverse the IRS only by renegotiating the IRS with the counterparty.Older IRS's that may be on the books may be obsolete and add “noise” toa party's balance sheet.

It would be desirable to provide processes and methods for converting ornetting outdated swaps.

SUMMARY

Systems and methods for converting open positions for over-the-counterswaps to standardized forward interest rate swaps (IRS), such ascentrally cleared swaps, are disclosed. The disclosed systems andprocesses are not limited to open positions derived or resulting fromIRS transactions or any particular over-the-counter financialinstruments. Instead, the systems and processes may be generally appliedto any negotiable financial instruments and investment vehicles. In oneexemplary embodiment, innovations for converting IRS positions tocentrally cleared IRS products are disclosed.

In one embodiment, a method of converting an over-the-counter swapassociated with a fixed rate and a floating rate to a forward swap isdisclosed. The method includes determining a spot rate estimate betweena spot rate associated with an over-the-counter swap and a spot rateassociated with a forward swap, determining a spot payout based on thespot rate estimate and a notional amount, calculating a market valueassociated with the over-the-counter swap payments, calculating a marketvalue based on the spot rate estimate, calculating a market value basedon a fixed rate, and determining a cash flow difference between themarket value based on the spot rate estimate and the market value basedon a fixed rate.

In another embodiment, a method of converting an over-the-counter swaphaving a fixed rate leg and a floating rate leg to a forward swap isdisclosed. The method includes (a) determining a notional value of acoupon to be received on an agreed-upon start date for anover-the-counter swap and discounting the notional value of the couponto a spot date, (b) determining a cash flow as a difference between thefixed rate leg and the floating rate leg applied from a last coupon dateto the next spot coupon agreed-upon date, (c) calculating a market valueof the fixed leg for payments, (d) calculating the market value of adesired forward fixed or floating leg discounted back to today. Themethod further includes calculating a mark-to-market for converting thisover-the-counter spot swap to an equivalent a forward swap according tothe market value of the coupon determined in (a) the market value of theremaining coupons on the fixed leg in (c) and the market value of thedesired floating leg (d).

The details of these and other embodiments of the present invention areset forth in the accompanying drawings and the description below. Otherembodiments are disclosed, and each of the embodiments can be used aloneor together in combination. Additional features and advantages of thedisclosed embodiments are described in, and will be apparent from, thefollowing description and figures.

BRIEF DESCRIPTION OF THE DRAWINGS

The present invention may take physical form in certain parts and steps,embodiments of which will be described in detail in the followingdescription and illustrated in the accompanying drawings that form apart hereof, wherein:

FIG. 1 illustrates a computer network system that may be used toimplement aspects of the disclosure;

FIG. 2 illustrates an example of a conversion method implementedaccording to aspects of the disclosure;

FIG. 3 illustrates another example of a conversion method implementedaccording to aspects of the disclosure; and

FIG. 4 illustrates a flowchart detailing an algorithm that may beimplemented according to aspects of the disclosure.

DETAILED DESCRIPTION

An example of a suitable operating environment 100 in which variousaspects of the invention may be implemented is shown in FIG. 1. Theoperating environment 100 is only one example of a suitable operatingenvironment and is not intended to suggest any limitation as to thescope of use or functionality of the invention. A computer system 102may be configured for operation within the operating environment 100.The computer system 100 may include a processor or processing unit 104and a memory or memory unit 106. The memory or memory unit 106 may beconfigured to store computer-executable instructions in accordance withaspects of the invention. The computer-executable instructions may, inturn, be executed by the processor or processing unit 104. Thecomputer-executable instructions may be comprised of modules inaccordance with aspects of the invention.

The computer system 102 may be in communication with one or moreinput/output (I/O) devices 108. The I/O devices 108 may be, for example,a keyboard, a mouse, voice automation, a screen or display, a kiosk, ahandheld computing device display, a microphone, etc. The computersystem 102 may be configured for communication with a network 110. Thenetwork 110 may be a secure virtual private network (VPN), the Internet,a wireless network such as an IEEE 802.11x network, anEthernet-compatible network, or any other secure or non-securecommunication configuration or system.

A database 112, which may be a third-party database, may be configuredto contain, for example, information such as the LIBOR rate or otherinformation useful in determining market values of derivative products.The database 112 may be connected through the network 110 to thecomputer system 102. Similarly, one or more computing devices 114 suchas, for example, a laptop computer, a handheld computing device, or anyother mobile computing device may be connected through the network 110to the computer system 102. In one embodiment, a user of a computingdevice 114 can remotely communicate via the network 110 to computersystem 102 which may be located or connected to a clearinghouse orexchange. A user may remotely enter orders for agreements offered by theexchange and indicate a bank account to pay margin requirements andreceive cash flows from swaps.

Of course, numerous additional servers, computers, handheld devices,personal digital assistants, telephones and other devices may also beconnected to exchange computer system 102. Moreover, one skilled in theart will appreciate that the topology shown in FIG. 1 is merely anexample and that the components shown in FIG. 1 may be connected bynumerous alternative topologies.

The clearinghouse which may store and/or control the computing system102 may act as a third-party guarantor of an agreement for a derivative,such as an exchange traded or exchange listed derivative, between thetwo parties of the agreement. For example, the derivative may be acentrally cleared forward swap. At least one benefit of an exchangetraded derivative, as opposed to the OTC type, is that the derivative iscleared and guaranteed by the clearinghouse. This may promise moreinteresting capital efficiencies for institutions that may cross-marginone derivative against another derivative.

I. Conversion of Swaps

In an embodiment, one or more existing swaps may be converted to astandardized forward swap. A clearing process may be initiated todetermine positions with converted swaps and to process the cash flowsresulting from the conversion. The clearing process may be initiated by,for example, the processing unit 104 operating within the computersystem 102. Following the initial cash flow processing, the positionsassociated with converted swaps will be maintained and guaranteed by acentral clearing party. As the IRS positions for all parties may bestandardized, the floating rate reset and payment processing may besimpler and easier to manage because there is only one floating ratereset and cash flow calendar per currency. The International Swaps andDerivatives Association (ISDA) day-count conventions, affect of holidaysand other cash flow and reset related parameters may also bepre-selected.

Customers with OTC spot swaps can choose to convert their OTC spot swapsto a centralized or standardized forward swaps such as those offeredChicago Mercantile Exchange Inc. (CME). Conversion from the OTC swap toa centralized or standardized forward swap may provide a number ofbenefits such as, but limited to, favorable asset treatment, netting,hedging/margining credits and better Basis Point Value (BPV)/Duration(the value of a 1 basis point change in yield) and duration matching totheir balance sheets. Different methods may be utilized CME offers twomethods for converting OTC spots swaps to forward swaps.

A. Accrued Interest Method—Agreed Floating Rate

FIG. 2 illustrates an example of an accrued interest method 200 that maybe utilized to convert an OTC swap to a standardized swap by marking tomarket the OTC swap to the closest equivalent standardized swap. Todetermine the closest equivalent standardized swap for a specific OTCswap, a payout of the next coupon from the date the swap counterpartiesbring in their OTC swap for conversion must be determined. Uponcompletion of the conversion, both parties to the original OTC swap areexposed only to a series of forward rates. This is in contrast to thecase when the parties had an OTC swap where they were exposed to aseries of forward rates and a spot rate.

TABLE 1 r spot rate f forward rate df discount factor dx date on periodx r(0,3) the spot rate that applies from period 0 until period 3 f(3,6)the forward rate that applies from period 3 until period 6 df(0,3) thediscount factor that applies from period 0 until period 3

Table 1 provides a description and definition of the factors andvariables related to the accrued interest method 200 illustrated in FIG.2. In particular, these factors and variables are utilized as a part ofcomputations and steps of the accrued interest method 200. Thecomputations utilized to convert the OTC swap to a standardized forwardswap include three difficulties that may need addressing: (1) if the OTCswap coupon dates are non-International Monetary Market (IMM) dates; (2)if the OTC swap payment frequency is not the same as that of thestandardized swaps; and (3) If the spot rate (r(−1,3) in the Table 1above, and illustrated in FIG. 2) for the OTC swap is not agreed upon ornot determined by the counterparties.

For the sake of initially illustrating and discussing the method 200, itwill be assumed that: (a) all OTC swap coupon dates are IMM dates; and(b) all OTC swap payment frequencies are the same as that of thestandardized swaps. Returning to the example illustrated in FIG. 2, itmay be assumed that the parties to the OTC swap have agreed or definedthe floating rate. Thus, the rate (then r(−1,3) is known) then thepayout may be calculated as follows:

$\begin{matrix}{{{Payout}\mspace{14mu} {of}\mspace{14mu} {Spot}\mspace{14mu} {Coupon}}=={\left\lbrack {{r\left( {{OTC}\mspace{14mu} {fixed}\mspace{14mu} {rate}} \right)} - {r\left( {{- 1},3} \right)}} \right\rbrack*}} \\{{{{df}\left( {0,3} \right)}*{\left( {{d\; 3} - {d\; 1}} \right)/360}*}} \\{{{Notional}\mspace{14mu} {Amount}}} \\{= {\left\lbrack {{r\left( {{OTC}\mspace{14mu} {fixed}\mspace{14mu} {rate}} \right)} - {r\left( {{- 1},3} \right)}} \right\rbrack*}} \\{{{SVF}\mspace{14mu} {of}\mspace{14mu} 3\mspace{14mu} {month}\mspace{14mu} {standardized}\mspace{14mu} {swap}*}} \\{{{Notional}\mspace{14mu} {Amount}}}\end{matrix}$

Where, the SVF is the sum of the day count adjusted discount factors ofthe swap yield curve to a desired maturity. Additional details relatedto the SVF are discussed and described in the incorporated U.S. patentapplication Ser. No. 11/950,117, filed on Dec. 4, 2007, and titled“FACTORIZATION OF INTEREST RATE SWAP VARIATION”.

B. Accrued Interest Method—Implied Floating Rate

There may be occasions where the rate may not be known or determined.For example, the parties may not agree to a rate. The rate may beestimated or calculated by: (i) determining the spot rate read fromLIBOR/EURIBOR fixings on the spot date (0 in FIG. 2)(corresponding tozero (0) to three (3) month rate r(0,3) illustrated in FIG. 2); (ii)Determining the spot rate read from LIBOR/EURIBOR fixings on the lastcoupon date (−1 in diagram above) (corresponding to the rate r(−1,0)illustrated in FIG. 2); (iii) The rates determined in (i) and (ii) maybe combined to imply a more up-to-date rate from period identifiedbetween −1 to 3 in FIG. 2 utilizing the formula:

$r_{{- 1},3} = \left\lbrack \left( {1 + {r_{{- 1},0}*\left( \frac{d_{0} - d_{- 1}}{360} \right)*\left( {1 + {r_{0,3}*\left( \frac{d_{3} - d_{0}}{360} \right)} - 1} \right\rbrack*\frac{360}{\left( {d_{3} - d_{- 1}} \right)}}} \right. \right.$

The formula may be utilized to determine or estimate the rate r(−1,3)based on the known interest rates at r(−1) and r(0,3). Thus, the rater(−1,3) may be implied to determine the forward interest rate.

The determined or estimated rate r(−1,3) may, in turn, be utilized todetermine the payout:

$\begin{matrix}{{{Payout}\mspace{14mu} {of}\mspace{14mu} {Spot}\mspace{14mu} {Coupon}}=={\left\lbrack {{r\left( {{OTC}\mspace{14mu} {fixed}\mspace{14mu} {rate}} \right)} - {r\left( {{- 1},3} \right)}} \right\rbrack*}} \\{{{{df}\left( {0,3} \right)}*{\left( {{d\; 3} - {d\; 1}} \right)/360}*}} \\{{{Notional}\mspace{14mu} {Amount}}} \\{= {\left\lbrack {{r\left( {{OTC}\mspace{14mu} {fixed}\mspace{14mu} {rate}} \right)} - {r\left( {{- 1},3} \right)}} \right\rbrack*}} \\{{{SVF}\mspace{14mu} {of}\mspace{14mu} 3\mspace{14mu} {month}\mspace{14mu} {standardized}\mspace{14mu} {swap}*}} \\{{{Notional}\mspace{14mu} {Amount}}}\end{matrix}$

Once this payout is made, the mark-to-market (MTM) on the remaining partof the OTC swap with the standardized swap may be determined. Basically,at this point, the method 200 involves marking to market the series ofexpected forward rates of the OTC swap to the series of expected forwardrates of the standardized swap. The marking to market process of themethod 200 may be determined as:

Payout  of  Remaining  Expected  Series =  = Market  Value  of  Remaining  OTC  Fixed  Leg − MV  of  standardized  swap  fixed  leg

Applying the marking to market process to the example illustrated inFIG. 2 yields:

Market  Value  of  the  standardized  Swap  Fixed  Leg = (df(0, 9) − df(0, 3)) * NotionalMarket  Value  of  Remaining  OTC  Fixed  Leg =  = r(OTC  fixed  rate) * [df(0, 6) * (d 6 − d 3)/360 + df(0, 9) * (d 9 − d 6)/360] * Notional$\begin{matrix}{{{Total}\mspace{14mu} {Market}\mspace{14mu} {to}\mspace{14mu} {Market}\mspace{14mu} {Payout}}=={{{Payout}\mspace{14mu} {of}\mspace{14mu} {Spot}\mspace{14mu} {Coupon}} +}} \\{{{Payout}\mspace{14mu} {of}\mspace{14mu} {Remaining}\mspace{14mu} {Expected}\mspace{14mu} {Series}}} \\{= {{\left( {r_{{- n},9}^{fixed} - r_{{- 1},3}} \right)*{df}_{0,3}*\left( \frac{d_{3} - d_{1}}{360} \right)} +}} \\{{{r_{{- n},9}^{fixed}\begin{bmatrix}{{{df}_{0,6}*\left( \frac{d_{6} - d_{3}}{360} \right)} +} \\{{df}_{0,9}*\left( \frac{d_{9} - d_{6}}{360} \right)}\end{bmatrix}} -}} \\{\left\lbrack {{df}_{0,3} - {df}_{0,9}} \right\rbrack} \\{= {{r_{{- n},9}^{fixed}\begin{bmatrix}{{{df}_{0,3}*\left( \frac{d_{3} - d_{1}}{360} \right)} +} \\{{{df}_{0,6}*\left( \frac{d_{6} - d_{3}}{360} \right)} +} \\{{df}_{0,9}*\left( \frac{d_{9} - d_{6}}{360} \right)}\end{bmatrix}} -}} \\{{\left\lbrack {r_{{- 1},3}*{df}_{0,3}*\left( \frac{d_{3} - d_{6}}{360} \right)} \right\rbrack -}} \\{\left\lbrack {{df}_{0,3} - {df}_{0,9}} \right\rbrack} \\{= {{MarketValueofOTCfixedleg} -}} \\{{{{MV}\mspace{14mu} {of}\mspace{14mu} {AccruedFloatingCoupon}} -}} \\{{{MV}\mspace{14mu} {of}\mspace{14mu} {ForwardFixedorFloatingLeg}}}\end{matrix}$

FIGS. 3 and 4 illustrate another example of the accrued interest method200 illustrated in FIG. 2. In particular, the exemplary method 300 ofFIG. 3 is discussed in detail and illustrated in the flowchart of FIG.4.

At block 400, the exemplary method 300 may be initiated by determiningthe notional/cash value of the coupon to be received on the IMM startdate (e.g., Jun. 20, 2007) and discounting that amount back to the spotdate. As previously discussed and shown above, the cash flow may bedetermined as the difference between the OTC spot swap fixed rate andthe floating rate applied from the last coupon date (e.g., Mar. 21,2007) to the next spot coupon IMM date (e.g., Jun. 20, 2007). If thefloating rate is agreed upon by the parties then the cash flow can beeasily determined and discounted. If not then floating rate from lastcoupon date to IMM start date may be implied.

At block 402, the market value of the fixed leg for payments made onSep. 19, 2007 and Dec. 19, 2007 per the agreed upon fixed ratediscounted back to the spot date (e.g., Apr. 1, 2007) may be calculated.

At block 404, the market value of the desired standardized fixed orfloating leg covering the forward rates from Jun. 20, 2007 to Sep. 19,2007 and from Sep. 19, 2007 to Dec. 19, 2007 discounted back to todaymay be calculated.

At block 406, the market value of the coupon (step 400) may be combinedwith the market value of the remaining coupons on the fixed leg (step402) and the total of these two market values may be subtracted from themarket value of the desired floating leg (Standardized Forward Swapfloating leg) (step 404). The resulting product of this combinationrepresent the Mark to Market (MTM) necessary for converting this OTCspot swap to an equivalent standardized forward swap.

At block 408 the MTM product may be evaluated. If the total MTM ispositive, the OTC fixed leg has a greater market value than the fixedleg of the desired standardized forward swap (plus the additional OTCspot accrued floating coupon) and then at block 410, the floating legholder must pay the fixed leg holder that amount to induce them toconvert. However, if the total MTM is negative, the OTC fixed leg has alower market value than the fixed leg of the desired StandardizedForward Swap (plus the additional OTC spot accrued floating coupon) andthen, at block 412 the fixed leg holder must pay the floating leg holderthat amount to induce them to convert.

C. Forward Conversion Method

The forward conversion method builds on the accrued interest method 200disclosed and discussed above. The forward conversion method converts anOTC swap with a certain maturity to a standardized swap with a differentmaturity than that of the OTC swap.

Initially the forward conversion method determines the payout of thespot coupon per the accrued interest method 200 discussed above. Theforward conversion method is generally an attempt to quantify theincreased risk in the first MTM collection made. After the risk isquantified, the MTM process adjusts the fixed rate from “yesterday” to“today's” settlement rate for the same maturity standardized swap. Toquantify the risk: (1) a reasonable approximation to the closest/mostcomparable instrument may be made, and the approximation may becollected through the MTM process; or (2) the duration and convexitycosts may be directly calculated and then added to the coupon that wasdetermined for the parties.

The accrued interest method 200 suggests that all the forward rates forthe OTC and standardized swap are aligned with each other including thelast forward rate of the original OTC swap matches the last forward rateof the standardized swap. This is a simplifying assumption that can bebroken and the MTM differences be calculated using the methods shownbelow. The matching relationship is not necessarily the case when theparties attempt to trade or convert their original OTC swaps for a new,longer maturity standardized swap.

In one embodiment, the remaining portion of the OTC swap may beevaluated after the payout is determined. Returning to the example shownin FIG. 2, after the payout the fixed leg of OTC swap looks as follows:

$r_{{- n},9}^{fixed}\left\lbrack {{{f_{0,6}}*\left( \frac{d_{6} - d_{3}}{360} \right)} + {{f_{0,9}}*\left( \frac{d_{9} - d_{6}}{360} \right)}} \right\rbrack$

If, for example, it was desirable to covert the OTC swap maturing inperiod 9 to a standardized swap maturing in period 12. Thus the fixedleg of the Standardized swap looks like:

$r_{3,12}^{fixed}\left\lbrack {{{f_{3,6}}*\left( \frac{d_{6} - d_{3}}{360} \right)} + {{f_{3,9}}*\left( \frac{d_{9} - d_{6}}{360} \right)} + {{f_{3,12}}*\left( \frac{d_{12} - d_{9}}{360} \right)}} \right\rbrack$

In this example, the fixed leg equals the floating leg of thestandardized swap which looks like:

$= {{f_{3,6}*{f_{3,6}}*\left( \frac{d_{6} - d_{3}}{360} \right)} + {f_{6,9}*{f_{3,9}}*\left( \frac{d_{9} - d_{6}}{360} \right)} + {f_{9,12}*{f_{3,12}}*\left( \frac{d_{12} - d_{9}}{360} \right)}}$

Thus the OTC swap leg covers the floating rate series up to period 9,whereas the standardized swap covers the floating rate series up toperiod 12, i.e., up to period 9 plus the floating rate from period 9 to12 as illustrated by the following (note all the discount factors beloware LIBOR/EURIBOR discount factors not standardized swap discountfactors as used above):

$f_{9,12}*\left( \frac{d_{12} - d_{9}}{360} \right)$

Discounting this back to the swap start date of period 3 provides:

$f_{9,12}*\left( \frac{d_{12} - d_{9}}{360} \right)*{f_{3,12}}$

Discount this back to a present day, being period 0 provides:

${f_{9,12}*\left( \frac{d_{12} - d_{9}}{360} \right)*{f_{3,12}}*{f_{0,3}}} = {f_{9,12}*\left( \frac{d_{12} - d_{9}}{360} \right)*{f_{0,12}^{{Libor}/{Euribor}}}}$

Thus, to get a comparable OTC swap to the standardized swap an extracoupon is added to the OTC swap to construct a theoretical equivalent ofthe standardized swap. The floating rate from period 9 to 12 f_(9,12)may be read from the LIBOR/EURIBOR fixing curve read on day 0 wheref_(9,12)the implied forward is

$\frac{f_{0,12}}{f_{0,9}} = {{f_{9,12}} = {\frac{1}{\left( {1 + {f_{9,12}*\frac{d_{12} - d_{9}}{360}}} \right)} = {{> f_{9,12}} = {\left( {\frac{f_{0,9}}{f_{0,12}} - 1} \right)*\frac{360}{\left( {d_{12} - d_{9}} \right)}}}}}$

Thus, the following may be added to the remaining OTC swap Fixed Leg:

$f_{9,12}*\left( \frac{d_{12} - d_{9}}{360} \right)*{f_{0,12}^{{Libor}/{Euribor}}}$

${{Market}\mspace{14mu} {Value}\mspace{14mu} {of}\mspace{14mu} {Remaining}\mspace{14mu} {Comparable}\mspace{14mu} {OTC}\mspace{14mu} {swap}\mspace{14mu} {Fixed}\mspace{14mu} {Leg}} = {{r_{{- n},9}^{fixed}\left\lbrack {{{f_{0,6}}*\left( \frac{d_{6} - d_{3}}{360} \right)} + {{f_{0,9}}*\left( \frac{d_{9} - d_{6}}{360} \right)}} \right\rbrack} + {f_{9,12}*\left( \frac{d_{12} - d_{9}}{360} \right)*{f_{0,12}^{{Libor}/{Euribor}}}}}$$\begin{matrix}{\begin{matrix}{{{Market}\mspace{14mu} {Value}\mspace{14mu} {of}\mspace{14mu} {Standardized}}\mspace{14mu}} \\{{swap}\mspace{14mu} {Fixed}\mspace{14mu} {Leg}}\end{matrix} = {r_{3,12}^{fixed}\begin{bmatrix}{{{f_{0,6}}*\left( \frac{d_{6} - d_{3}}{360} \right)} +} \\{{{f_{0,9}}*\left( \frac{d_{9} - d_{6}}{360} \right)} +} \\{{f_{0,12}}*\left( \frac{d_{12} - d_{9}}{360} \right)}\end{bmatrix}}} \\{= {{f_{3,6}*{f_{0,6}}*\left( \frac{d_{6} - d_{3}}{360} \right)} + {f_{6,9}*{f_{0,9}}*}}} \\{{\left( \frac{d_{9} - d_{6}}{360} \right) + {f_{9,12}*{f_{0,12}}*\left( \frac{d_{12} - d_{9}}{360} \right)}}} \\{= \left\lbrack {{f_{0,3}} - {f_{0,12}}} \right\rbrack}\end{matrix}$ $\begin{matrix}{\begin{matrix}{{{Payout}\mspace{14mu} {of}\mspace{14mu} {Remaining}}\mspace{11mu}} \\{{Expected}\mspace{14mu} {Series}}\end{matrix}=={\begin{matrix}{{Market}\mspace{14mu} {Value}\mspace{14mu} {of}\mspace{14mu} {Remaining}} \\{{OTC}\mspace{14mu} {Fixed}\mspace{14mu} {Leg}}\end{matrix} -}} \\{{{MV}\mspace{14mu} {of}\mspace{14mu} {Standardized}\mspace{14mu} {swap}\mspace{14mu} {Fixed}\mspace{14mu} {Leg}}} \\{= {{r_{{- n},9}^{fixed}\left\lbrack {{{f_{0,6}}*\left( \frac{d_{6} - d_{3}}{360} \right)} + {{f_{0,9}}*\left( \frac{d_{9} - d_{6}}{360} \right)}} \right\rbrack} +}} \\{{{f_{9,12}*\left( \frac{d_{12} - d_{9}}{360} \right)*{f_{0,12}^{{Libor}/{Euribor}}}} -}} \\{\left\lbrack {{f_{0,3}} - {f_{0,12}}} \right\rbrack}\end{matrix}$${{Total}\mspace{14mu} {Market}\mspace{14mu} {to}\mspace{14mu} {Market}\mspace{14mu} {Payout}}=={{{Payout}\mspace{14mu} {of}\mspace{14mu} {Spot}\mspace{14mu} {Coupon}} + {{Payout}\mspace{14mu} {of}\mspace{14mu} {Remaining}\mspace{14mu} {Expected}\mspace{14mu} {{Series}\left( {r_{{- n},9}^{fixed} - r_{{- 1},3}} \right)}*{f_{0,3}}*\left( \frac{d_{3} - d_{1}}{360} \right)} + {r_{{- n},9}^{fixed}\left\lbrack {{{f_{0,6}}*\left( \frac{d_{6} - d_{3}}{360} \right)} + {{f_{0,9}}*\left( \frac{d_{9} - d_{6}}{360} \right)}} \right\rbrack} + {f_{9,12}*\left( \frac{d_{12} - d_{9}}{360} \right)*{f_{0,12}^{{Libor}/{Euribor}}}} - \left\lbrack {{f_{0,3}} - {f_{0,12}}} \right\rbrack}$

In another embodiment, the payout of the remaining expected series byvaluing the market value of the remaining OTC Fixed Leg may beapproximated as follows:

One way to quantify the convexity and duration risk associated withswitching from an OTC swap to a standardized swap is two track theduration and convexity of the swap. The duration and convexity of thefixed leg of the standardized swap may be computed using the followingTaylor series approximation of the change in market value:

dp/p = −D *dy + ½ * C * dy{circumflex over ( )}2 where: dy = change inthe yield to maturity (YTM) of the fixed leg (from OTC fixed leg YTM toCME fixed leg YTM) D = modified duration of fixed leg of OTC swap C =convexity of fixed leg of OTC swap P = Price of fixed leg of OTC swap dp= expected change in market value on fixed leg of OTC swap given thechange in yield to maturity.

${{Market}\mspace{14mu} {Value}\mspace{14mu} {of}\mspace{14mu} {Remaining}\mspace{14mu} {Comparable}\mspace{14mu} {OTC}\mspace{14mu} {swap}\mspace{14mu} {Fixed}\mspace{14mu} {Leg}}=={{r_{{- n},9}^{fixed}\left\lbrack {{{f_{0,6}}*\left( \frac{d_{6} - d_{3}}{360} \right)} + {{f_{0,9}}*\left( \frac{d_{9} - d_{6}}{360} \right)}} \right\rbrack} + {p}}$${{{Payout}\mspace{14mu} {of}\mspace{14mu} {Remaining}\mspace{14mu} {Expected}\mspace{14mu} {Series}}=={{{Market}\mspace{14mu} {Value}\mspace{14mu} {of}\mspace{14mu} {Remaining}\mspace{14mu} {OTC}\mspace{14mu} {Fixed}\mspace{14mu} {Leg}} - {{MV}\mspace{14mu} {of}\mspace{14mu} {Standardized}\mspace{14mu} {swap}\mspace{14mu} {Fixed}\mspace{14mu} {Leg}}}} = {{r_{{- n},9}^{fixed}\left\lbrack {{{f_{0,6}}*\left( \frac{d_{6} - d_{3}}{360} \right)} + {{f_{0,9}}*\left( \frac{d_{9} - d_{6}}{360} \right)}} \right\rbrack} + {p} - \left\lbrack {{f_{0,3}} - {f_{0,12}}} \right\rbrack}$${{Total}\mspace{14mu} {Market}\mspace{14mu} {to}\mspace{14mu} {Market}\mspace{14mu} {Payout}}=={{{Payout}\mspace{14mu} {of}\mspace{14mu} {Spot}\mspace{14mu} {Coupon}} + {{Payout}\mspace{14mu} {of}\mspace{14mu} {Remaining}\mspace{14mu} {Expected}\mspace{14mu} {{Series}\left( {r_{{- n},9}^{fixed} - r_{{- 1},3}} \right)}*{f_{0,3}}*\left( \frac{d_{3} - d_{1}}{360} \right)} + {r_{{- n},9}^{fixed}\left\lbrack {{{f_{0,6}}*\left( \frac{d_{6} - d_{3}}{360} \right)} + {{f_{0,9}}*\left( \frac{d_{9} - d_{6}}{360} \right)}} \right\rbrack} + {p} - \left\lbrack {{f_{0,3}} - {f_{0,12}}} \right\rbrack}$

D. Non-IMM Based Swaps

Non-IMM dated swaps can also be converted via the above methods. Forexample, a non-IMM dated swap with the payment frequency the same as thestandardized swaps' payment frequencies can be converted by shifting theOTC swap coupon payments present value to the present value of thecoupon payments had they occurred on an IMM date. One way of doing thisis as follows:

Non-IMM Dated OTC swap:

${{{r_{{- n},9.5}^{fixed}\left\lbrack {{{f_{0,3.5}}*\left( \frac{d_{3.5} - d_{1.5}}{360} \right)} + {{f_{0,6.5}}*\left( \frac{d_{6.5} - d_{3.5}}{360} \right)} + {{f_{0,9.5}}*\left( \frac{d_{9.5} - d_{6.5}}{360} \right)}} \right\rbrack}<>r_{{- 1.5},3.5}}*{f_{0,3.5}}*\left( \frac{d_{3.5} - d_{- 1.5}}{360} \right)} + {f_{3.5,6.5}*{f_{0,6.5}}*\left( \frac{d_{6.5} - d_{3.5}}{360} \right)} + {f_{6.5,9.5}*{f_{0,9.5}}*\left( \frac{d_{9.5} - d_{6.5}}{360} \right)}$${{Payout}\mspace{14mu} {of}\mspace{14mu} {Spot}\mspace{14mu} {Coupon}} = {\left( {r_{{- n},9.5}^{fixed} - r_{{- 1.5},3.5}} \right)*{f_{0,3.5}}*\left( \frac{d_{3.5} - d_{1.5}}{360} \right)}$${{Remaining}\mspace{14mu} {Expected}\mspace{14mu} {Series}\mspace{14mu} {of}\mspace{14mu} {non}\text{-}{IMM}\mspace{14mu} {Dated}\mspace{14mu} {OTC}\mspace{14mu} {swap}} = {{{{{r_{{- n},9.5}^{fixed}\left\lbrack {{{f_{0,6.5}}*\left( \frac{d_{6.5} - d_{3.5}}{360} \right)} + {{f_{0,9.5}}*\left( \frac{d_{9.5} - d_{6.5}}{360} \right)}} \right\rbrack}<>f_{3.5,6.5}}*{f_{0,6.5}}*\left( \frac{d_{6.5} - d_{3.5}}{360} \right)} + {f_{6.5,9.5}*{f_{0,9.5}}*\left( \frac{d_{9.5} - d_{6.5}}{360} \right)}} = {{f_{0,3.5}} - {f_{0,9.5}}}}$

Desired standardized swap:

${{{r_{{- n},9}^{fixed}\left\lbrack {{{f_{0,6}}*\left( \frac{d_{6} - d_{3}}{360} \right)} + {{f_{0,9}}*\left( \frac{d_{9} - d_{6}}{360} \right)}} \right\rbrack} = {{{f_{3,6}*{f_{0,6}}*\left( \frac{d_{6} - d_{3}}{360} \right)} + {f_{6,9}*{f_{0,9}}*\left( \frac{d_{9} - d_{6}}{360} \right)}} = {{f_{0,3}} - {f_{0,9}}}}}{Payout}\mspace{14mu} {of}\mspace{14mu} {Remaining}\mspace{14mu} {Expected}\mspace{14mu} {Series}\mspace{14mu} {to}\mspace{14mu} {non}\text{-}{aligned}\mspace{14mu} {dates}} = {{r_{{- n},9.5}^{fixed}\left\lbrack {{{f_{0,6.5}}*\left( \frac{d_{6.5} - d_{3.5}}{360} \right)} + {{f_{0,9.5}}*\left( \frac{d_{9.5} - d_{6.5}}{360} \right)}} \right\rbrack} - \left\lbrack {{f_{0,3.5}} - {f_{0,9.5}}} \right\rbrack}$

This MTM means that the fixed and floating legs of the OTC swap areequal.

Payout of Remaining Expected Series to aligned dates

=[df _(0,3,5) −df _(0,9,5) ]+dp−[df _(0,3) −df _(0,9)]

Where dp is the market value differential due to duration and convexitybias of the OTC fixed leg to the CME fixed leg.

dp/p=−D*dy+½*C*dŷ2

dp is estimated per method 2 above.

$\begin{matrix}{\begin{matrix}{{{Total}\mspace{14mu} {Market}\mspace{14mu} {to}}\mspace{14mu}} \\{{Market}\mspace{14mu} {Payout}}\end{matrix} = {{{Payout}\mspace{14mu} {of}\mspace{14mu} {Spot}\mspace{14mu} {Coupon}} +}} \\{{{Payout}\mspace{14mu} {of}\mspace{14mu} {Remaining}\mspace{14mu} {Expected}\mspace{14mu} {Series}}} \\{= {{{Payout}\mspace{14mu} {of}\mspace{14mu} {Spot}\mspace{14mu} {Coupon}} +}} \\{{\begin{matrix}{{Payout}\mspace{14mu} {of}\mspace{14mu} {Remaining}\mspace{14mu} {Expected}\mspace{14mu} {Series}} \\{{to}\mspace{14mu} {non}\text{-}{aligned}\mspace{14mu} {dates}}\end{matrix} +}} \\{\begin{matrix}{{Payout}\mspace{14mu} {of}\mspace{14mu} {Remaining}\mspace{14mu} {Expected}\mspace{14mu} {Series}} \\{{to}\mspace{14mu} {aligned}\mspace{14mu} {dates}}\end{matrix}} \\{= {{\left( {r_{{- n},9.5}^{fixed} - r_{{- 1.5},3.5}} \right)*{f_{0,3.5}}*\left( \frac{d_{3.5} - d_{1.5}}{360} \right)} +}} \\{{{r_{{- n},9.5}^{fixed}\left\lbrack {{{f_{0,6.5}}*\left( \frac{d_{6.5} - d_{3.5}}{360} \right)} + {{f_{0,9.5}}*\left( \frac{d_{9.5} - d_{6.5}}{360} \right)}} \right\rbrack} -}} \\{{\left\lbrack {{f_{0,3.5}} - {f_{0,9.5}}} \right\rbrack + \left\lbrack {{f_{0,3.5}} - {f_{0,9.5}}} \right\rbrack +}} \\{{{p} - \left\lbrack {{f_{0,3}} - {f_{0,9}}} \right\rbrack}} \\{= {{\left( {r_{{- n},9.5}^{fixed} - r_{{- 1.5},3.5}} \right)*{f_{0,3.5}}*\left( \frac{d_{3.5} - d_{1.5}}{360} \right)} +}} \\{{{r_{{- n},9.5}^{fixed}\left\lbrack {{{f_{0,6.5}}*\left( \frac{d_{6.5} - d_{3.5}}{360} \right)} + {{f_{0,9.5}}*\left( \frac{d_{9.5} - d_{6.5}}{360} \right)}} \right\rbrack} +}} \\{{{p} - \left\lbrack {{f_{0,3}} - {f_{0,9}}} \right\rbrack}}\end{matrix}$

E. Non-Aligned Coupon Dates

Non-aligned coupon dated swaps can also be converted via the abovemethods. A non-aligned coupon dated swap can be performed similar to thenon-IMM dated case. One way is to first strip out the first coupon andpay it out. The dp may be calculated in relation to the fixed leg andadded to the market value of the remaining expected series. Finally, theresulting product may, in turn, be added to the first coupon payout andsubtract the net from the market value of the desired standardized swapfloating leg. An example of this is shown below:

Total Market to Market Payout

=Payout of Spot Coupon+Payout of Remaining Expected Series

$= {{\left( {r_{{- n},16.5}^{fixed} - r_{{- 1},6.5}} \right)*{f_{0,6.5}}*\left( \frac{d_{6.5} - d_{1.5}}{360} \right)} + {r_{{- n},16.5}^{fixed}\left\lbrack {{{f_{0,9.5}}*\left( \frac{d_{9.5} - d_{6.5}}{360} \right)} + {{f_{0,16.5}}*\left( \frac{d_{16.5} - d_{9.5}}{360} \right)}} \right\rbrack} + {p} - \left\lbrack {{f_{0,3}} - {f_{0,16}}} \right\rbrack}$

Where dp is the market value differential due to duration and convexitybias of the OTC fixed leg to the CME fixed leg.

dp/p = −D *dy + ½ * C * dy{circumflex over ( )}2 where: dy = change inthe yield to maturity (YTM) of the fixed leg (from OTC fixed leg YTM toCME fixed leg YTM) D = modified duration of fixed leg of OTC swap C =convexity of fixed leg of OTC swap P = Price of fixed leg of OTC swap dp= expected change in market value on fixed leg of OTC swap given thechange in yield to maturity.

F. Overriding the Standardized Swap Curve with Other Curves

The standardized swap curve can be overridden in favor of any other swapcurve. The adjustments necessary would simply involve recalculating theSwap Value Factor using the rates from the new curve. The swap valuefactor is the sum of the discount factors implied from the swap curve,so in case of using a new curve the new SVF is:

${NewSVF} = \left\lbrack {{{f_{0,3}}*\left( \frac{d_{3} - d_{1}}{360} \right)} + {{f_{0,6}}*\left( \frac{d_{6} - d_{3}}{360} \right)} + {{f_{0,9}}*\left( \frac{d_{9} - d_{6}}{360} \right)}} \right\rbrack$

where the discount factors (df's) come from the new swap curve.

Clients can have several methods of implying a “more accurate” swapcurve with “more accurate” rates that imply interest rate, liquidity andbasis risks “better”. Several of these methods are itemized below;however clients may have different proprietary algorithms of derivingthose swap yield curves. As mentioned above, regardless of the method,if clients agree to use their own swap curves, all the methods shownabove hold true. The difference is that a new SVF needs to be calculatedas shown in the equation above. This new SVF would have to use thediscount factors calculated from the rates which the clients send usfrom their swap yield curve.

The common methods clients may use to build their swap yield curves are:Term structure methods, such as Hull-White, Vasicek, Black-Derman Toy(BDT) etc. These methods are divided into:

Short rate models which attempt to predict what the continuouslycompounding short rate (the rate over an infinitesimally small period oftime starting from today and maturing at an infinitesimally small periodof time from today). The models rely on attempting to calibrate to thereal market price of risk based on today's spot yield curve and thenaccounting for one or several factors, hence the models are consideredone, two or three factor models, depending on how many factors are used.The factors can be: (a) short interest rates; (b) stochastic volatility;(c) stochastic means; and (d) stochastic mean reversion parameters. Inaddition instead of simply assuming that the short rates move accordingto a stochastic process, certain models such as BDT assume that thereare only two possible realizations of the short rates either up(increasing) or down (decreasing). These models build a binomial tree ofall the possible interest rates, a.k.a. a lattice, and then will usesthose rates to imply the term structure. Other models can buildtrinomial trees of the short rates, up, down or flat (no change).

Forward rate models which instead of assuming that the short rates moveaccording to a stochastic process, these models assume that the forwardrates will move according to a stochastic process. An example of such amodel is Heath-Jarrow-Morton model (HJM).

Principal Component Analysis which instead of modeling the short/forwardrates these models look at the level, slope and curvature of the yieldcurve and attempt to imply the best possible combination to provide themost accurate rates.

The present invention has been described herein with reference tospecific exemplary embodiments thereof. It will be apparent to thoseskilled in the art that a person understanding this invention mayconceive of changes or other embodiments or variations, which utilizethe principles of this invention without departing from the broaderspirit and scope of the invention as set forth in the appended claims.

1. A computer-implemented method of converting an over-the-counter swapassociated with a fixed rate and a floating rate to a forward swap, themethod comprising: determining a spot rate estimate between a spot rateassociated with an over-the-counter swap and a spot rate associated witha forward swap; determining a spot payout based on the spot rateestimate and a notional amount; calculating a market value associatedwith the over-the-counter swap payments; calculating a market valuebased on the spot rate estimate; calculating a market value based on afixed rate; and determining a cash flow difference between the marketvalue based on the spot rate estimate and the market value based on afixed rate.
 2. The method of claim 1, wherein determining the spot rateestimate is based on an agreed upon rate.
 3. The method of claim 1,wherein determining the spot rate estimate includes estimating the spotrate estimate based on two or more known spot rates.
 4. The method ofclaim 3, wherein estimating the spot rate includes estimating the swaprate based on a swap rate curve.
 5. The method of claim 1, wherein theover-the-counter swap has a first maturity and the forward swap has asecond maturity different from the first maturity.
 6. The method ofclaim 1, wherein the over-the-counter swap and the forward swap are bothInternational Monetary Market dated swaps.
 7. A computer-implementedmethod of converting an over-the-counter swap having a fixed rate legand a floating rate leg to a forward swap, the method comprising: (a)determining a notional value of a coupon to be received on anagreed-upon start date for an over-the-counter swap and discounting thenotional value of the coupon to a spot date; (b) determining a cash flowas a difference between the fixed rate leg and the floating rate legapplied from a last coupon date to the next spot coupon agreed-upondate; (c) calculating a market value of the fixed leg for payments; (d)calculating the market value of a desired forward fixed or floating legdiscounted back to today; and (e) calculating a mark-to-market forconverting this over-the-counter spot swap to an equivalent a forwardswap according to the market value of the coupon determined in (a) themarket value of the remaining coupons on the fixed leg in (c) and themarket value of the desired floating leg (d).
 8. The method of claim 7,wherein determining the cash flow is based on an agreed upon ratefloating rate.
 9. The method of claim 7, wherein determining the cashflow includes estimating a spot rate based on two or more known spotrates.
 10. The method of claim 9, wherein estimating the spot rateincludes estimating the swap rate based on a swap rate curve.
 11. Themethod of claim 7, wherein the over-the-counter swap has a firstmaturity and the forward swap has a second maturity different from thefirst maturity.
 12. The method of claim 7, wherein the agreed-upon startdate is an International Monetary Market start date.
 13. Acomputer-implemented method of converting an over-the-counter swaphaving a first leg and a second leg to a forward swap, the methodcomprising: determining a payout to be received on a start date of anover-the-counter swap and discounting the payout to a spot date;determining a cash flow as a difference between the first leg and thesecond leg applied from a last payout date to the next payout date;calculating a market value of the first leg; calculating a market valueof a forward swap having a first and second legs, wherein the first andsecond legs are discounted to the start date; and calculating amark-to-market for converting the over-the-counter spot swap to theforward swap as a function of the payout, the market value of the firstleg and the market value of the second leg associated with the forwardswap.
 14. The method of claim 13, wherein determining the cash flow isbased on an agreed upon rate floating rate.
 15. The method of claim 13,wherein determining the cash flow includes estimating a spot rate basedon two or more known spot rates.
 16. The method of claim 15, whereinestimating the spot rate includes estimating the swap rate based on aswap rate curve.
 17. The method of claim 13, wherein theover-the-counter swap has a first maturity and the forward swap has asecond maturity different from the first maturity.
 18. The method ofclaim 13, wherein the agreed-upon start date is an InternationalMonetary Market start date.